Potential Scaling in Density Functional Theory

TL;DR

This paper introduces a conjugate potential scaling in density functional theory, establishing exact relations for density functionals evaluated on different potentials, and demonstrates these on simple ion series.

Contribution

It defines a new conjugate potential scaling in DFT, providing exact relations that enhance understanding of density functional behavior under scaling.

Findings

Derived exact relations for density functionals under potential scaling

Illustrated conditions on two- and four-electron ions

Enhanced theoretical framework for density functional approximations

Abstract

Density scaling has a rich history in density functional theory, providing exact conditions for use in the construction of ever more accurate approximations to the unknown exchange-correlation functional. We define a conjugate potential scaling for each density scaling. This provides exact relations on various important density functionals, in particular, relating functionals evaluated on exact densities of different potentials. We illustrate these conditions on the two- and four-electron ion series.